Which scenario could be represented by this graph?

A. Lanie steadily fills a cup of water, stopping when it is almost full.
The x-axis represents time; the y-axis represents the amount of
water.
O B. Lanie lights a candle. After 15 minutes, she puts it out. Half an
hour later, she lights it again. The x-axis represents time; the y-axis
represents the height of the candle.
O C. Lanie steadily fills a cup of water. The x-axis represents time; the
y-axis represents the amount of water.
OD. The temperature in Lanie's backyard drops steadily over time as a
cold front moves in. The x-axis represents time; the y-axis
represents the temperature.

The required probability by using multinomial distribution is 0.03.

The multinomial distribution is the kind of probability distribution used in finance to assess factors like the likelihood that a company would declare earnings that are greater than anticipated while rivals report disappointing results. In a multinomial distribution, a process has a set of k potential outcomes (X1, X2, X3,..., Xk) and corresponding probabilities (p1, p2, p3,..., pk) such that Σpi = 1. Due to the certainty of one of the outcomes, the probabilities must add up to 1.

Given that at the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late.

Multinomial probability P = [ n! / ( n1! * n2! * ... nk! ) ] * ( p1n1 * p2n2 * . . . * pknk )

= [ 6! / ( 1! x 3! x 2! x 0! ) ] * ( 0.10^1 x  0.70^3 x 0.12^2 x 0.08^0)

=60*0.000494

=0.02964

Therefore the required probability = 0.03

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To make a volume of 320mL mixture that contains 8% vinegar, use 64mL of the first brand and 256mL of the second brand.

Let F be the volume of the first brand and let S be the volume of the second brand.

Now, we want the total mixture to be 320mL so: F + S = 310

Also, you want the total mixture to contain 12% vinegar so:

0.08F + 0.13S = 0.12(320)

Now, we can solve the system of equations using substitution method.

F + S = 320   -----(1)

0.08F + 0.13S = 0.12(320)   -----(2)

F = 320 - S      [solve 1st equation for F]

0.08(320 - S) + 0.13S = 0.12(320)     [substitute into 2nd equation]

25.6 - 0.08S + 0.13S = 38.4

0.05S = 12.8

S = 256 mL

F + 256 = 320     [substitute answer for S back into original equation]

F = 320 - 256

F = 64 mL

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The GCF of a set of values (typically two) is the greatest factor that applies to every number.

We must find the GCF of 18 and 24:

List the factors of both values:

Let's identify the common factors between 18 and 24:

Therefore, the GCF is 6.

The greatest length that Liz can make using the strings is 6 cm.

Answer:

E

Step-by-step explanation:

We just need the last two clues. Since they said it is a line (4th clue) it could only be B, C, or E. But then, the last clue says the domain is -7. Now for almost all lines the domain is 'all real numbers'. All kinds of diagonal lines and also horizontal lines, the domain is all real numbers. Only vertical lines have a domain that is a single value. Graph E is a line that has the domain -7.

The best possible Upper Estimate for the distance travelled is 69 .

In the question ,

a graph is given ,

we have to estimate the possible upper estimate ,

the time period [0,5] is divided into 5 sub intervals ,

that is (0,1) , (1,2) ,(2,3) , (3,4) and (4,5) .

From the graph we see that ,

the upper limit of the distance in the interval (0,1) is = 20 .

the upper limit of the distance in the interval (1,2) is = 17 .

the upper limit of the distance in the interval (2,3) is = 13 .

the upper limit of the distance in the interval (3,4) is = 10 .

the upper limit of the distance in the interval (4,5) is = 9 .

adding all the upper limit ,

we get ,

upper estimate is = 20 + 17 + 13 + 10 + 9 = 69

Therefore , the upper estimate of the distance is 69 .

The given question is incomplete , the complete question is

compute the best possible upper estimate for the distance he travels over this period when dividing [0, 5] into 5 equal subintervals and using endpoint sample points .

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Step-by-step explanation:

the standard form is (x - h)² = 4p(y - k), where the focus is (h, k + p) and the directrix is y = k - p.

the vertex is exactly in the middle between focus and directrix, and is therefore (h, k) = (0, 0).

therefore, p = 9.

(x - 0)² = 4×9×(y - 0)

x² = 36y

y = 1/36 x²

The standard error of the mean is e = 0.2 and the 95% confidence interval is 9 ± 0.392.

Given:

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours.

a.

σ = 1.8

n = 81

we know that,

standard error of the mean e = σ/[tex]\sqrt{n}[/tex]

= 1.8/[tex]\sqrt{81}[/tex]

= 1.8/9

= 18/10/9

=  18*1/10*9

= 2*1/10

= 2/10

= 0.2

b.

confidence interval CI = x ± Z*s/√n

= 9 ± 1.9600*1.8/√81

= 9 ± 0.392

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Answer:

What is the question?!

Step-by-step explanation:

The radius of the circle is approx. 17.692

What is a radius?

In traditional geometry, the radius of a circle or sphere is any line segment that connects the object's center to its perimeter; in more modern usage, the radius also refers to the length of those segments.

To put it another way, the radius of a circle is the distance between any two points on the circle's circumference. Usually, "R" or "r" is used to indicate it.

Solution Explained:

Given,

Length of cord = 12cm

Length from the center of the circle = 13cm

We use the formula,

r = [tex]\sqrt{12^2 + 13^2}[/tex]

 = [tex]\sqrt{144 + 169}[/tex]

 = [tex]\sqrt{309}[/tex]

 ≈ 17.692

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The solution of the equation x²-x -3 = 0 are x = (1±√13) /2.

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

Here we are given the equation x²-x -3 = 0 ---(i) which is a quadratic equation which we can solve using Sri Dharacharya Method.

Sri Dharacharya Formula:   For a quadratic equation ax² + bx + c = 0

The value of x is x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) /2a.

Using this formula in (i), we get

     x = (-(-1) ± [tex]\sqrt{(-1)^{2} -4*1*(-3)}[/tex]) /2*1

⇒  x = (1±√13) /2.

The solution of the equation are irrational which are x = (1±√13) /2.

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Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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The true statement for the relation is, the order of rows is unimportant.

What is row and column?

A row is an arrangement of items that are put next to or horizontally. A vertical split of items based on category is known as a column. The arrangement is in a left to right direction. The set-up is vertical, from top to bottom.

A table's rows are individual groups of connected data. Rows and columns are found in tables in relational databases (also known as records and fields, respectively).

Consider the given statements,

Entities in a column vary as to kind.

The order of the columns is important.

The order of the rows is unimportant.

More than one column can use the same name.

From the given statements, the true statement for the relation is, the order of rows is unimportant.

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Answer:

1500 : 5000

Step-by-step explanation:

Answer:

The ratio is 3: 7

Step-by-step explanation:

You turn the 5 kg into grams so they are both the same unit. So that's 5,000 grams. 1,500 grams was the amount taken out. Then what is left is 3,500. So it makes the ratio 1,500: 3,500. Then you simplify it to 3:7.

I hope this helps!!!

Please mark me brainliest :)

The Side-Angle-Side rule is used to demonstrate the congruent theorem of a particular collection of triangles.

The two sides and included angle of ABDA are therefore equivalent to ABDC's two sides and included angle. According to the SAS Triangle Congruence Theorem, the triangles are congruent.

Knowing merely angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent. There are four shortcuts that can be used to check whether two triangles are congruent.

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The area of the triangle according to the information given in the  question is 17/8.

A triangle is a three-sided polygon that is also known as the trigon.

Angles in a triangle are formed by connecting the three sides end to end at a point.

Consider the following right-angled triangle, with vertices (0,-4), (0.0), and (1,0).

Its legs are 4 and 1 meters long, and its hypotenuse is 42+12=17 meters long.

The height "h" (altitude) of this triangle drawn to the hypotenuse is easily determined.

Based on the area, we get the equation (41)/2=(1/2)17h h=4/17 h=0.970143.

As we can see, it is not a single unit.

It means that the triangle's legs should be 17/4 as long as the original triangle's legs (1 unit and 4 units).

As a result, the area of the seeking triangle is (1/2)(17/4)(417/4) = (1/2)(17/4) =17/8

As a result, the area of the triangle in the question is 17/8.

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If a car gets 13 kilometers per liter of gasoline,  miles per gallon of gasoline would it get is 40 miles.

if a car gets 13 kilometers per liter of gasoline,

We need to find the number of miles per gallon of gasoline would it get

1 gallon of gasoline = 3.78541 liters of gasoline

In 1 liters of gasoline car travels = 13 kilometers

In 3.78541 liters of gasoline, the car travels 13 x 3.785 = 49.2kilometers

1,60934 kilometer = 1 mile

49.2 kilometers = (1/1.60934) x 49.2 = 40 miles

Therefore, if a car gets 13 kilometers per liter of gasoline,  miles per gallon of gasoline would it get is 40 miles.

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The rug has a dimension of 6 by 9 yards.

What is a dimension?

In everyday language, a dimension is a measurement of an object's length, width, and height, such as a box. The concept of dimension in mathematics is a continuation of the ideas that a line is one dimension, a plane is two dimensions, and space is three dimensions.

Dimensions include things like width, depth, and height. Three geometric objects have one dimension each: a line, a square, and a cube.

Solution Explained:

Given in question

Area of the room = 9*12=108 yards^2

Area of 1/2 the room = 180/2 = 90 yards^2

So according to the question, the rug covers half the room so we form the equation and we simplify,

(9-2X)(12-2X)=54

108-24X-18X+4X^2=54

4X^2-42X+108-54=0

4X^2-42X+54=0

(2X-18)(2X-3)=0

2X-3=0

2X=3

X=3/2

X=1.5

(9-2*1.5)(12-2*1.5)=54

(9-3)(12-3)=54

6*9=54

54=54

The rug has dimensions of 6 by 9 yards.

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The number of goals scored by one team is 56 and the other team scored 79 goals.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let the number of goals scored by one team be 'x' and the number of goals scored by the other team be 'y'

One team scored 23 goals more than another team

                        y = x + 23 --------(I)

And both teams scored 135 goals in total, so

                        x + y = 135 ------(II)

ut the value of y = x + 23 in equation (II), we get

                    x + x + 23 = 135

                   2x = 135 - 23

                    x = 112/2

                    x = 56

then y = 79.

Hence, the number of goals scored by one team is 56 and the other team scored 79 goals.

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The concept and examples of congruence are described below.

The word 'congruent' signifies 'precisely equivalent' concerning shape and size. In any event, when we turn, flip, or pivot the shapes, they stay equivalent. For instance, draw two circles of similar range, then cut them out and put them on each other.

congruent angles have a similar point measure. For instance, an ordinary pentagon has five sides and five points, and each point is 108 degrees. No matter what the size or size of a customary polygon, the points will constantly be compatible.

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When 2 angles and an included side of 1 triangle are congruent to the corresponding piece of another triangle, it is said to be in ASA or AAS congruency

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle DEF by the Angle-Side-Angle Postulate.

Contrarily, the Angle-Angle-Side Postulate (AAS) states that two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle PQR by the Angle-Angle-Side Postulate.

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The equation of parabola that open upwards with focus 6 units is x²=24y.

A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point  (the focus) and a fixed straight line (the directrix).

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.

The general equation of Parabola is given by

y = a(x-h)²+ k

where (h,k) is the vertex of parabola.

And the equation of parabola open upward is,

(x-h)² = 4a(y-k)

where (h,k) is vertex and a is focus unit.

⇒ (x-0)² = 4(6)(y-0)

⇒ x² = 24y

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The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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The equation 5x - (3 - 2x) = -(-x- 7) + 6x is an equation with no solution. It simplifies to 0 = 10

How to simplify an equation with no solution?

An equation with no solution is a type of equation that is never true, no matter what we replace the variable with e.g.  6x + 10 = 6x - 10. This equation has no solution because is no value that will ever satisfy this type of equation

Given:  the equation 5x - (3 - 2x) = -(-x- 7) + 6x

5x - (3 - 2x) = -(-x- 7) + 6x

Clear the parenthesis:

5x - 3 + 2x = x + 7 + 6x

Add/subtract like terms:

7x -3 = 7x + 7

Collect like terms:

7x -7x = 7 + 3

0 = 10

Since 0 is not equal to 10, therefore this expression has no solution

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Answer:

1. C) [tex]3.6 \, \textrm{cm}[/tex]

2. A) [tex]4\sqrt{10}[/tex]

Step-by-step explanation:

Utilize the Pythagorean Theorem for both problems:

[tex]a^2+b^2=c^2[/tex]

where [tex]a[/tex] and [tex]b[/tex] are the right triangle's legs (short sides adjacent to the right angle) and [tex]c[/tex] is its hypotenuse.

1) Form an equation using the above formula.

[tex]8.7^2 + x^2 = 9.4^2[/tex]

Next, isolate x.

[tex]x^2 = 9.4^2 - 8.7^2[/tex]

[tex]x = \sqrt{9.4^2 - 8.7^2}[/tex]

Finally, plug the square root into a calculator and round the result to get:

C) [tex]3.6 \, \textrm{cm}[/tex]

2) Form an equation using the Pythagorean Theorem.

[tex]6^2 + x^2 = 14^2[/tex]

Next, isolate x.

[tex]x^2 = 14^2 - 6^2[/tex]

[tex]x^2 = 196 - 36[/tex]

[tex]x^2 = 160[/tex]

[tex]x = \sqrt{160}[/tex]

Finally, use prime factorization to simplify the square root.

[tex]x = \sqrt{10 \cdot 16[/tex]

[tex]x = \sqrt{(2 \cdot 5) \cdot 2^4}[/tex]

[tex]x = 2^2 \sqrt{2 \cdot 5}[/tex]

A) [tex]4\sqrt{10}[/tex]

Answer:

rate of the boat is 10.5 and the rate of the current is 1.5

Step-by-step explanation:

Distance = rate x time

Let r = rate of the boat

Let c = current

Upstream:

Rate: r -c

Time: 4 hours

Distance: 36

36 = 4(r-c)  Divide both sides of the equation by 4

9 = r - c

Downstream:

Rate: r + c

Time: 3 hours

Distance: 36

36 = 3(r+c)  Divide both sides by 3

12 = r -c

Combine the two bold equations:

9 = r - c

12 = r + c

21 = 2r  Divide both side's by 2

10.5 = r This is the rate of the boat.

Rate of the current:

4(10.5 - c) =36

42 - 4x = 36  Subtract 42 from both sides

-4x = -6  Divide both sides by -4

x = 3/2 or 1.5

There are many types of functions as;

1. Injective function

2. Many – one function.

3. Onto – function (Surjective Function)

4. Into – function.

5. Polynomial function.

6. Linear Function.

7. Identical Function.

8. Quadratic Function.

What is Function?

A relation between a set of inputs having one output each is called a function.

Now,

The name of the functions are;

There are many types of functions as;

1. Injective function

2. Many – one function.

3. Onto – function (Surjective Function)

4. Into – function.

5. Polynomial function.

6. Linear Function.

7. Identical Function.

8. Quadratic Function.

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1. F v (D → T)

2.  V F

3. D

∴ T

4. D → T (Disjunctive syllogism 1,2)

5. T          ( Modus Ponens 3,4)

2. P → (cu → T)

2. Q → (T → E)

3. P

4. Q

∴ Cu → E

5. Cu → T  (modus ponens 1,3)

6. T → E  ( modus ponens 2,4)

7. Cu → E (Hypothetical syllogism 5,6)

3. 1. ~ X → [~X → (y → X)]

   2. ~ X

   ∴ ~ y

  3. ~X → (y → X)   (modus ponens 1,2)

  4.  y → X              ( modus ponens 2,3)

  5. ~ y                     ( modus tollens 2,4)

4. 1. k → (L→m)

    2. m v k

    3. ~m

    ∴ ~L

    4. K   (disjunctive syllogism 2,3)

    5. L → m  (modus ponens 1,4)

    6. ~ L    (modus tollens 3,5)

5. 1. ~S → D

   2. ~S v (~D→K)

   3. ~ D

∴ K

  4. ~(~S)   (Modulas tollens 1,3)

  5. S          ( Double nojection 4)

  6. ~D→K (Disjunctive syllogism 2,5)

  7. K         (Modus ponenes 3,6)

Hence we get the required answer.

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The required value of the sample standard deviation of given data is 62.895.

A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. Low standard deviation implies information are grouped around the mean, and exclusive expectation deviation demonstrates information are more fanned out.

Using the formula:

Where: xi = sample value; μ = sample mean; n = sample size

Calculate the mean first:

μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5

  = 102 / 5

μ = 20.4

Then, Using the mean, calculate (xi - μ)² for each value:

(12.0 - 20.4)² = 70.56

(18.3 - 20.4)² = 4.41

(29.6 - 20.4)² = 84.64

(14.3 - 20.4)² = 37.21

(27.8 - 20.4)² = 54.76

Sum the squared differences and divide by n - 1.

μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76

  = 251.58 / 5-1

μ = 62.895

Thus, required  the sample standard deviation for these data is 62.895.

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The lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex].

What is the Lower bound and Upper bound?

Lower Bounds - The lowest value that would be utilized to round a number to the previously estimated value is known as the lower bound.

Upper Bounds - The lower value that would be used to round a number to the next expected value is known as the upper bound.

Given, length = 370 mm

           width = 19.4 mm

First, we consider length = 370 mm, then

The upper bound for length = 375 mm

And, the lower bound = 365 mm

Second, we consider  width = 19.4 mm, then

The upper bound for width = 19.45 mm

And, the lower bound = 19.35 mm

So, the area of the given rectangle is:

Area =  length * width

Using lower bounds dimensions for both length and width, then

Area = 365*19.35 [tex]mm^{2}[/tex]

        = 7062.75 [tex]mm^{2}[/tex]

Therefore, the lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex]

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The correct responses for the linear and exponential functions are;

An exponential function is  one that has the argument as an exponent

1. The functions in the question are;

y = 4ᵃ + 1 and y = -2·x + 7

A linear function is of the form, y = m·x + c

Where;

m = The slope

c = The y-intercept

By comparison, the y-intercept of the linear function is 7

2. The standard form of the exponential function is; y = a·bᵃ + q

Where the y-intercept is a + q

The y-intercept of the exponential function is therefore;

y = 4⁰ + 1 = 1 + 1 = 2

The y-intercept of the exponential function is 2

3. The solution can be obtained from the equation;

4ᵃ + 1 = -2·x + 7, we get;

4ᵃ = -2·x + 7 - 1 = -2·x + 6

When x = 1,

4¹ = -2×1 + 6 = 4

The number of points of intersection obtained by plotting the functions is 1

4. The y-value of the solution is therefore;

y = 4¹ + 1 = 5

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