Determine if x and y are inversely proportional. If applicable, find the constant of variation.

The area of the triangle is 48 square units.

To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.

Length of side BC = 9+3 = 12 units

Length of side CA = 3+5 = 8 units

Length of side BA = 9+5 = 14 units

Area of triangle = (1/2 × Base × Height) square units

Area of triangle ACB = 1/2 × CA× BC sq units

                          Area = 1/2 × 8 × 12 = 48 sq units

Hence, the area of triangle ACB is 48 square units.

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Answer:

47.91 units²

Step-by-step explanation:

The radius of each circle is:

Therefore, the side lengths of the triangle are:

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:

[tex]\implies s=\dfrac{14+12+8}{2}=17[/tex]

To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:

[tex]\implies A=\sqrt{17(17-14)(17-12)(17-8)}[/tex]

[tex]\implies A=\sqrt{17(3)(5)(9)}[/tex]

[tex]\implies A=\sqrt{2295}[/tex]

[tex]\implies A=47.906158268...[/tex]

[tex]\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)[/tex]

The number of bags of grass seed that Amanda should use to spread her yard is 16.65 bags, meaning she needs to buy not more than 17 bags, using mathematical operations.

The basic mathematical operations we use are subtraction, addition, division, and multiplication.

In this situation, we use the division operation.

The division operation involves four parts:

The area of the yard = 4,995 ft²

1 yard = 3 feet

Area of the yard = 1,665 square yards(4,995/3)

The number of bags per 100 square yards = 1 bag

For 1,665 square, the number of bags = 16.65 bags (1,665 ÷ 100)

Thus, Amanda requires 16.65 bags of the grass seed for her yard.

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The error interval for the time spent to complete the race is 12.305 ≤ t < 12.315

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

Distance = 100 m

Time = 12.31 seconds

From the question, we understand that

Time = rounded to the nearest hundredth of a second.

The highest number that can be rounded to 12.31 to the nearest hundredth is 12.314

While the least is 12.305

When represented as an interval, we have

12.305 ≤ t < 12.314

Add/subtract the error

So, we have

12.305 - 0.001 ≤ t < 12.314 + 0.001

Evaluate

12.305 ≤ t < 12.315

Hence, the error interval is 12.305 ≤ t < 12.315

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The correct answer to how many different ways he can draw is 24.

optimal solution is arrived with value of variables as :

x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0

minimize cost:

z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆=2x

subject to:

20x₁+30x₂+40x₃+40x₄+45x₅+30x₆ ≥70 : amount of protein

50x₁+30x₂+20x₃+25x₄+50x₅+20x₆ ≥100 : amount of carbohydrate

4x₁+9x₂+11x₃+10x₄+9x₅+10x₆ ≥20 : amount of fat

where x₁, x₂, x₃, x₄, x₅, x₆ are units of 6 foods

solution using Simplex method:

After introducing artificial variables:

Min Z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆+0S₁+0S₂+0S₃+MA₁+MA₂+MA₃

subject to

20x₁+30x₂+40x₃+40x₄+45x₅+30x₆-S₁+A₁ ≥ 70

50x₁+30x₂+20x₃+25x₄+50x₅+20x₆-S₂+A₂≥ 100

4x₁+9x₂+11x₃+10x₄+9x₅+10x₆-S₃+A₃=20

and x₁,x₂,x₃,x₄,x₅,x₆,A₁,A₂,A₃≥0

Refer to the image for Z

Since all Zj-Cj≤0

Hence, optimal solution is arrived with value of variables as :

x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0

Min Z=7.2727

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The adult dose for the decongestant is 2.7 milligrams.

The information can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since for a 45-pound child, the adult dose should be multiplied by 0.3, When the child's dose of a decongestant is 9 milligrams, the adult dose will be:

= Children dose × 0.3

= 9 × 0.3

= 2.7

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If one of the 55 students is selected at random, the probability of this occurring can be written as a fraction by dividing the number of selected students by the total number of students. In this case, the probability would be 1/55.

We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

Given that,

The following frequencies are found for the number of pips up when the die comes to rest, assuming a die is tossed 1000 times. Find out if there is proof that this die is not symmetrical using the chi-squared goodness of fit test. The standardized residuals should be noted.

x₁           x₂           x₃           x₄         x₅           x₆

163        178        142        150       183        184

We know that,

          observed       expected         Op-Ep         (Op-Ep)²/Ep

x₁          163                 166.7                -3.7               0.082

x₂          178                 166.7                 11.3              0.7659

x₃          142                 166.7                -24.7            3.6598

x₄          150                 166.7                -16.7             1.673

x₅          183                 166.7                16.3               1.5938

x₆           184                 166.7               17.3               1.7954

                                                                                 -----------

                                                                                 9.5699

Expected = 1/nΣXa=1/6(1000)=166.7

Therefore, We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

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The true statements are they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

The box plot is also called box-and-whisker plot.

The data is divided into sections by box plots, with each section containing around 25% of the total data.

Box plots are useful as:

They offer a visual overview of the data,

making it simple for researchers to spot skewness,

the dispersion of the data set.

The minimum value, first quartile, median, third quartile, and maximum value are the five values that make up a box plot.

And they don't include mean.

From the above discussion,

we have three statements that are true and those statements are;

they help describe sets of data, they show the data split into four parts and each section of a box plot represents 25% of the data.

Therefore, the correct statements are A, C and E.

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Answer: $1.48

Step-by-step explanation:

find how much each gallon cost

1. 17.76/3=5.92

Divide by 4 because 4 quarts equal a gallon

2. 5.92/4=1.48

Therefore each quart equals $1.48,

Hope this helps!

The given statement is FALSE.

Given statement;

When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure to effectively carry out and use the results.

The above-mentioned statement is FALSE.

→ We are aware that checking assumptions is crucial when applying statistics in daily life because failing to do so will prevent us from receiving fair answers to our statistical queries or drawing valid inferences. To use the good process and appropriate statistical distributions while utilizing statistics in daily life, it is crucial to examine assumptions.

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The radius of the sphere with the given point and the center is √238.

Here we have to find the radius of the sphere.

Given data:

The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).

The formula for the radius:

r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²

where (x1, y1, z1) = point on the center

(x2, y2, z2) = point on the sphere

Now putting the values we have

r² = (-4-2)² + ( -6-3)² + ( 10 +1)²

  =( -6)² +(- 9)²  + (11)²

  = 36 + 81 + 121

  = 238

r = √238.

Therefore the radius is √ 238.

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The product of the vectors v and w is gotten as; v ⋅ w = 22

We are given the vectors;

r = <8, 8, -6>

v = <3, -8, -3>

w = <-4, -2, -6>

We want to evaluate v.w which is a product of both vectors.

The formula will be;

v.w = (v_x * w_x) + (v_y * w_y) + (v_z * w_z)

Plugging in the values and solving gives;

v.w = (3 * -4) + (-8 * -2) + (-3 * -6)

v.w = -12 + 16 + 18

v.w = 22

We can conclude that the vector expressions has a product of 22

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The given

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

It is TRUE.

"Information available from the question:"

In the question:

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

It is TRUE / FALSE

Now, According to the question:

Let's know:

What is Frailty?

Frailty is most often defined as an aging-related syndrome of physiological decline, characterized by marked vulnerability to adverse health outcomes.

Incidence of multiple chronic conditions is connected to frailty, a condition marked by a lack of resilience to physiological changes and an elevated risk of poor health outcomes.

Hence, The above statement is TRUE.

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The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).

A factor is a number that divides another number, leaving no remainder.

Given is a polynomial, x³+3x²-x-3

x = -1 is the root of the polynomial, which it will completely divide the polynomial x³+3x²-x-3,

On dividing, we get,

(x³+3x²-x-3)÷(x+1) = (x²+2x-3)

Factorizing, (x²+2x-3), we get,

(x-1)(x+3)

Hence, The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).

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The number of elements in the direct product are 2.

What is direct product of groups?

The direct product, often written as G x H, is an operation used in group theory, a branch of mathematics, to create a new group from two existing ones. This operation, one of several crucial direct product concepts in mathematics, is the group-theoretic equivalent of the Cartesian product of sets.

Let, the number of elements of order 1 in  [tex]Z_1_6[/tex]  and  [tex]Z_1_9[/tex]  is 1.

Number of elements of order 2 in [tex]Z_1_6[/tex]  and [tex]Z_1_9[/tex]  are 1 and 0 respectively.

Number of elements of order 4 in [tex]Z_1_6[/tex]  and  [tex]Z_1_9[/tex] are 2 and 0 respectively.

Consider the table of number of elements of order.

                           Number of elements of order

                              1         2          4

           [tex]Z_1_6[/tex]              1         1           2

          [tex]Z_1_9[/tex]               1         0          0

Let x ∈ [tex]Z_1_6[/tex] x [tex]Z_1_9[/tex]

O(x) = lcm (O(a), O(b))

where x = (a, b)

That is, a ∈ [tex]Z_1_6[/tex]  and  b ∈ [tex]Z_1_9[/tex]  

Here only (4, 1) satisfies it and [tex]Z_1_6[/tex] has 2 elements of order 4 and [tex]Z_1_9[/tex]  has one element of order 1.

So,  [tex]Z_1_6[/tex] x [tex]Z_1_9[/tex] has 2 x 1 = 2 elements of order 4.

Hence, the number of elements in the direct product are 2.

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Complete question:

Complete question is attached below.

The number of capybaras that you will get after 14 days is given as follows:

3 capybaras.

Initially, the number of capybaras that you have is given as follows:

2 capybaras.

The pattern is then given as follows:

The time composed by 14 days is of 2 weeks, then the procedure will finish on the Monday 2 weeks from now.

The number of capybaras in that Monday than can be calculated step by step as follows:

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Answer:

Step-by-step explanation:

I forgot to add the last reason is AAS (two angles one side are congruent = triangles are congruent)

S.

1.Given

2. AE = EC

3. <AEB = <CED

4. <CDE = <ABE

5. triangles congruent

R.

1. Given

2. Segment bisector theorem

3. Vertical angles theorem

4. PAI Theorem

Hope this helps!

Answer:

[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]

Step-by-step explanation:

There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.

There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.

The only option that satisfies this is Option 1.

The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.

The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.

Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.

Hence , the graph of the function is plotted

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The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, an equation of the line that passes through (-1, 8) and is parallel to the line y = 6.

Slope of the parallel lines are equal to each other, therefore, solving for c,

8 = -1x0 + c

c = 8

Hence, The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

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After analyzing the given data we will get to know that all the options mentioned above are true.

A = BUC, B is a singleton set, and A = CU2 if A is the set of all prime numbers, B is the set of all even prime numbers, and C is the set of all odd prime numbers. Therefore, option D - All of the specified - is the answer to this question.

We've got

The entire set of prime numbers is A.

A = {2, 3, 5, 7, 11, 13}

B is a collection of even prime numbers.

B = {2}

C is a collection of all odd prime numbers.

C = {3, 5, 7, 11, 13,}

We are aware that the only even prime number is two. As a result, Set B is a singleton set because it only has one element.

Additionally, if we combine sets B and C, we will obtain set A, which contains all prime numbers.

Thus, we obtain A = B U C.

Since B = 2 is a singleton set, if we have A = B U C, we can also say A = C U 2.

Therefore, each of the aforementioned choices is appropriate.

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B can have a maximum value of 750.

Given info,

y ≤ - 15x + 3000

y ≤ 5x

What is the highest possible value of b in the XY plane if a point with the coordinates (a,b) is found in the system of inequalities above?

The maximum value of b occurs when taking equality.

⇒ - 15x + 3000 = 5x

⇒ - 20x = - 3000

⇒ - 20x = - 3000

⇒ x = 150

Therefore, y = 5 * 150

                    = 750

Hence, the maximum possible value of b = 750

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Equations have two complex solutions if their discriminant is negative. So, option A is the correct answer.

In algebra, the discriminant of any equation is a quantity that is used to find out about the nature of the roots using the formula = b²-4ac. It tells us if there are no solutions, one solution, or two.

Here, we have been told that the discriminant is negative.

From the formula, we can say that = D = b²-4ac < 0.

Here, if D<0, then x becomes an imaginary value. This means that the roots are going to be imaginary i.e., complex. Thus, the two roots that we get as a result of the formula are both going to be complex.

So, option A is the answer.

The complete that you might be looking for is given below.

If the discriminant of an equation is negative, which of the following is true of the equation

A. it has two complex solutions

B. it has one real solution

C. it had two real solutions

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Answer:

a.two complex solutions

Step-by-step explanation:

Howard Steele needs to invest  $117,817.77 today so that he may withdraw $12,000 each year for the next 20 years

Simple interest is often a predetermined percentage of the principal amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the equation, [tex]P = \frac{A\times(1-(1+r)^{-n}}{r}[/tex] the annuity, and the present value of money, P, can be connected.

P = 12000, r = 0.08 and n = 20.

∴ [tex]12000 = \frac{A\times(1-(1.08)^{-20}}{0.08}[/tex].

A = $117,817.77.

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|f(x) − f n(x)| = lim m→∞

|f m(x) − f n(x)| ≤ ϵ /2< ϵ

Converges Uniformly

A sequence of functions f n(x); n = 1, 2, 3,…. Is said to be uniformly convergent to f for a set E of values of x, if for each ε > 0, a positive integer N exists such that |f n(x) – f(x)| < ε for n ≥ N and x ∈ E.

A sequence (f n) of functions f n : A → R is uniformly Cauchy

on A if for every ϵ > 0 there exists N ∈ N such that

m, n > N implies that |f m(x) − f n(x)| < ϵ for all x ∈ A.

The key part of the following proof is the argument to show that a pointwise

convergent, uniformly Cauchy sequence converges uniformly.

A sequence (f n) of functions f n : A → R converges uniformly on

A if and only if it is uniformly Cauchy on A.

Suppose that ( f n) converges uniformly to f on A. Then, given ϵ > 0, there

exists N ∈ N such that

|f n(x) − f(x)| < ϵ/2

for all x ∈ A if n > N.

It follows that if m, n > N then

|f m(x) − f n(x)| ≤ |f m(x) − f(x)| + |f(x) − f n(x)| < ϵ for all x ∈ A,

which shows that (f n) is uniformly Cauchy.

Conversely, suppose that (f n) is uniformly Cauchy. Then for each x ∈ A, the

real sequence (f n(x)) is Cauchy, so it converges by the completeness of R. We

define f : A → R by

f(x) = limn→∞

f n(x),

and then f n → f pointwise.

To prove that f n → f uniformly, let ϵ > 0. Since (f n) is uniformly Cauchy,

can choose N ∈ N (depending only on ϵ) such that

|f m(x) − f n(x)| < ϵ /2

for all x ∈ A if m, n > N.

Let n > N and x ∈ A. Then for every m > N we have

|f n(x) − f(x)| ≤ |f n(x) − f m(x)| + |f m(x) − f(x)| < ϵ /2 + |f m(x) − f(x)|.

Since f m(x) → f(x) as m → ∞, we can choose m > N (depending on x, but it

doesn’t matter since m doesn’t appear in the final result) such that

|f m(x) − f(x)| < ϵ/2.

It follows that if n > N, then

|f n(x) − f(x)| < ϵ for all x ∈ A,

Then proves that f n → f uniformly

Alternatively, we can take the limit as m → ∞ in the Cauchy condition to get

for all x ∈ A and n > N that

|f(x) − f n(x)| = lim m→∞

|f m(x) − f n(x)| ≤ ϵ /2< ϵ

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The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.

The absolute maximum point is a point where the function obtains its greatest possible value.

And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.

Given equation is, f(x,y) = 3 + xy - x - 2y

we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).  

f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3

f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2

f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1

Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).

An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.

Given question is incomplete. Complete question is:

find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y  among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).

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(a) Class interval of a given data is 36.

(b) Frequency distribution is 44.

We have given that,

total frequency = 44

lower limit = $70

number of class = 5

(a) we have to find class interval,

Class interval =  [tex]\frac{Max. number - min. number}{no. of classes}[/tex]

here maximum number is 264 and minimum number is 84

Class interval = [tex]\frac{264 - 84}{5}[/tex]

                      = [tex]\frac{180}{5}[/tex]

Class interval = 36

we have to round our value to the next multiple of 5

so the class interval will be 40.

(b) A frequency distribution is the pattern of frequencies of a variable. It is the number of times each possible value of a variable occurs in a dataset. There are three types of frequency distribution such as Cumulative frequency distribution, Relative frequency distribution, Relative cumulative frequency distribution.  

The frequency distribution is as follows:

Class interval           Frequency

 70 - 110                         6

 111 - 151                          5

152 - 192                       10

193 - 233                       14

234 -  274                       9

Total                              44

This is the organize data into a frequency distribution.

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https://brainly.com/question/28367164

#SPJ4

Answer: they didnt distribute the 7 to the 4.5

Step-by-step explanation:

when distributing something outside of a parenthesis, you have to distribute it to all terms within the parenthesis, not just the variable