input
SOLIS
Output
4
S
7
Which ordered pair needs to be removed in order for
the mapping to represent a function?

The discounted price of an item did the price increased after the weekend by a fraction of 1/5.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.

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Null Hypothesis that is, the average errors for two processes differ significantly.

Two options being the same is the null hypothesis in inferential statistics. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

Always indicate the "null hypothesis" with an equal sign, and the alternative with a less-than, greater-than, or not equal sign. The researcher is looking for evidence that the two methods/processes produce different average errors since this alternative statement contains the not equal to symbol.

Hence, the correct pair of “null and alternative” hypotheses is given by,

[tex]Null Hypothesis(H0): UA = UB versus\\ H1: UA \neq UB; that is, the average .errors. for .two .processes .differ .significantly.[/tex]

[tex]"H0: UA = UB H1: UA \neq UB"[/tex]

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Answer:

$8 per pound

Step-by-step explanation:

16/2 = 8

Answer: $8

Step-by-step explanation:

16 divided by 2 = $8 per pound

The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.

Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.

So, Shannon's error:

In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:

The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.

Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

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Total 36 storage locations are allocated by the statement declare [tex]a[4,9][/tex] as integer.

The statement declare [tex]A[4,9][/tex] as integer allocates 4 × 9 = 36 storage locations for the array A. Each storage location is capable of holding a single integer value.

In this statement, the array A is declared with two dimensions, 4 and 9. The first dimension, 4, represents the number of rows in the array, and the second dimension, 9, represents the number of columns. This means that the array A has a total of 4 rows and 9 columns, for a total of 4 × 9 = 36 storage locations.

Here's an example of how the array A might be structured in memory:[tex]A[0,0] \ A[0,1] \ A[0,2] \ A[0,3] \ A[0,4] \ A[0,5] \ A[0,6] \ A[0,7] \ A[0,8]\\A[1,0] \ A[1,1] \ A[1,2] \ A[1,3] \ A[1,4] \ A[1,5] \ A[1,6] \ A[1,7] \ A[1,8]\\A[2,0] \ A[2,1] \ A[2,2] \ A[2,3] \ A[2,4] \ A[2,5] \ A[2,6]\ A[2,7] \ A[2,8]\\A[3,0] \ A[3,1] \ A[3,2] \ A[3,3] \ A[3,4] \ A[3,5] \ A[3,6] \ A[3,7] \ A[3,8][/tex]

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Answer:

1)

Step-by-step explanation:

[tex] {(x - 5)}^{2} = 38[/tex]

The required step solving the equation using Completing the square method is (x - 5)² = 38.

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

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.

We have the Equation: x² - 10x-13 = 0

Now, half the coefficient of x and add and subtract the square of the half of the coefficient of x.

So, x² - 10x-13 = 0

x² - 10x-13 -5² + 5² = 0

(x - 5)² - 25 - 13 = 0

(x-5)² -38= 0

(x - 5)² = 38

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The probability that Steph Curry makes the first 2 free throws and misses the last throw is 81/1000

Let A be the event that Steph Curry makes the free throw.

Let B be the event that Stech Curry does not make the free throw.

According to the problem,

P(A) = 90%

= 9/10

Since B is the complement of A,

P(B) = 1 - P(A)

= 1/10

Hee, Steph Curry gets 3 free throws. Hence, the probability that he makes the first 2 throws while he misses the third one is

P(A) X P(A) X P(B)

= 9/10 X 9/10 X 1/10

= 81/1000

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The probability of getting exactly 4 heads is 0.26

A loaded coin has 0.48 probability of coming up heads

0.52 probability of coming up tails.

coin is flipped 7 times

let's assume n = 7.

The seven flips of the coin are separate from one another, so what happens on one flip is unaffected by the outcomes of the other tosses.

When calculating the likelihood that two events will occur simultaneously, we must multiply the probabilities of events 1 and 2, presuming that event 1 occurred.

Tosses never affect one another, so the "assuming event 1 happened" part is no longer necessary because it has no effect on the probability. As a result, we just need to multiply the chances for each toss. This supposition is essential. We would have needed to know exactly how tosses are dependent on one another if they were interdependent.

Typically, we would have [tex](n! /(r!)*(n - r)!)*p^r*(1-p)^(n-r)[/tex] is the probability of getting r heads out of n, without taking into account the order.

probability of getting exactly 4 heads r = 4.

out of 7 flipping n =7.

7!/(4!*3!)   = 35

(0.48)^4 = 0.05308416

(0.52)^3 = 0.140608

35*0.05308416*0.140608 = 0.26124201492 = 0.26

so the probability of getting exactly 4 heads is 0.26.

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∫[tex]r(t)dt=[/tex][tex](0,t,\frac{t^2}{2} )+c[/tex] is accurate in its statement.

A definite integral whose limits are functions of the differential variable can be differentiated using Newton Leibniz Theorem's formula. Differentiation under the integral sign is another name for this. When limits are functions of the differential variable, the Newton Leibniz Theorem makes it simple to handle problems involving the differentiation of a definite integral.

Suppose that F(x) is a function whose derivative is f(x). Consequently, abf(x) dx = F(b) - F (a).

The Newton Leibniz Theorem can be used to determine the derivative of a definite integral when the limits of a definite integral are functions of t and the integrands are functions of x or vice versa.

As a result, statement C is the appropriate response.

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the truth table of expression (A+B).A is T ,T ,F,F . A truth table has one column for each input variable (such as P and Q) and a final column that lists all potential outcomes.

Truth tables are mathematical tables that are used in logic, specifically in relation to Boolean algebra, Boolean functions, and propositional calculus. They contain the functional values of logical expressions on each of their functional arguments, or more specifically, for each combination of values that their logical variables can take.

given

( A+B) . A

A          B      (A + B)      (A+B).A

T           T         T                  T

T           F         T                 T

F           T         T                 F

F           F         F                 F

So , the truth table of expression (A+B).A is T ,T ,F,F .

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The number of applicants that were not accepted are calculated to be 1260.

The number of applicants that were not accepted can be determined as follows;

Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;

360 × 9 / 2 = 3240 / 2 = 1620

Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.

The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;

Applicants not accepted = 1620 - 360

Applicants not accepted = 1260

Therefore 1260 applicants were not accepted by the program.

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The area of the ring between these two circles if the radius of the larger and the smaller circle is 10 and 6 is 200.96.

Given:

two circles have the same center $c.$

the larger circle has radius $10$

and the smaller circle has radius $6.$

we are asked to determine the  the area of the ring between these two circles.

⇒ Area of the ring =  Area of larger circle - area of smaller circle

⇒ Area of circle = πr²

⇒ Area of larger circle  = π(10)²

= 100π

⇒ Area of small circle = π(6)²

= 36π

Area of the ring =  Area of larger circle - area of smaller circle

Area of the ring = 100π - 36π

= 64π

= 200.96

Hence the area of the ring is 200.96

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Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .

A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."

The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.

Similar figures' surfaces have an area that is proportional to the square of their sides.

The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.

Keep in mind that the ratio of the sides is squared because we are working with areas.

[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]

Let area a smaller pentagon is a

[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]

a=[tex]\frac{98*4}{49}[/tex]

a= 8 [tex]in^{2}[/tex]

So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]

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Step-by-step explanation:

the volume of a pyramid is

base area × inner height / 3

we have the base area : 7×7 = 49 in²

so, we need to get the inner height h.

fit this we need to get the outer height l.

the surface area is

base area (49 in²) + 4×side triangle area = 185 in².

one of these 4 side triangle area is

baseline (7 in) × l / 2

so, we have a surface area

49 + 4×7×l/2 = 185

49 + 2×7×l = 185

49 + 14×l = 185

14×l = 136

l = 136/14 = 68/7 = 9.714285714... in

h we get now via Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.

l² = h² + 3.5²

94.36734694... = h² + 12.25

h² = 94.36734694... - 12.25 = 82.11734694...

h = 9.061862222... in

so, the volume of the pyramid is

49 × 9.061862222... / 3 = 148.0104163... in³ ≈

≈ 148.01 in³

Amrit's income is £27434.16.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let the Bethan's income be x

Amrit's income is 32% more than Bethan's income.

So, Amrit's income=x+32%

Amrit and Bethan's combined income is £54868.

According to given question we have

x+x+32%=£54868

2x+32/100=£54868

2x=54868-0.32

2x=54867.68

x=27433.84

Bethan's income=£ 27433.84

Amrit's income

=x+32%

=£ 27433.84+0.32

=£27434.16

Therefore,  Amrit's income is £27434.16.

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In equilateral triangle ABC, the length of side A is equal to the side B and side C.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees.

Here,

The length of side A of an equilateral triangle ABC is equal to the lengths of sides B and C.

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 y = 3/8x + 1/4 is equation of linear equation .

What in mathematics is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                   The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.

                 There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.

3/2x -4y+1=0

  -4y = -3/2x - 1

    y = 3/8x + 1/4

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The complete question is -

Which equation is equivalent to 3/2x -4y+1=0

Answer: 29%

Step-by-step explanation:

To find the percent of decrease, you need to first calculate the difference between the original cost and the current cost of the TV. You can do this by subtracting the current cost from the original cost: $700 - $500 = $200.

Next, divide the difference by the original cost and multiply by 100% to express the result as a percentage: ($200 / $700) * 100% = 28.57%.

Rounding this result to the nearest whole percent, we get that the percent of decrease is 29%.

Rounded to the nearest whole percent, the answer is 29%.

The expression when Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3 is 3(n + 4).

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.

In this scenario, Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3.

This will be:

= (n + 4) × 3

= 3(n + 4).

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Answer: 250 grams/packet = 8 packets.

Step-by-step explanation:

To find the number of 250g packets of biscuits that can be made from 2kg of biscuits, we need to first convert the weight of the biscuits to the same unit of measurement. Since 1 kilogram is equal to 1000 grams, 2kg of biscuits is equal to 2000 grams. Therefore, the number of 250g packets of biscuits that can be made from 2kg of biscuits is 2000 grams / 250 grams/packet = 8 packets.

Step-by-step explanation:

1 kg = 1000 g

as k stands for "kilo" meaning 1000.

250 g fit therefore 4 times into 1 kg.

and then 2×4 = 8 times into 2×1 = 2 kg.

so, there can be 8 250 g packets made from 2 kg.

The area of the triangle given in this problem is of:

A = 84 cm².

The area of a triangle of base b and height h is given by the multiplication of these two dimensions divided by two, which is equivalent to the multiplication of these measures by 0.5, hence:

Area = 0.5 x base x height.

For the triangle given at the end of the answer, these dimensions are given as follows:

Then the area of the triangle is obtained by the multiplication as follows:

Area = 0.5 x 8 x 21 = 4 x 21 = 84 cm².

The triangle from which we calculate the area is given by the image shown at the end of the answer.

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y=3 is the equation of a horizontal line that passes through the point (9, 3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If a line passes through a point (x₁, y₁) and has a slope of m, then the

equation of the line is given by (y-y₁) = m(x-x₁).  

Because the question states the line is horizontal, the slope is zero, or m=0.

Plugging the information into the slope equation gives:

(y-(3)) = 0(x-(9)).

y-3= 0

y= 3.

Hence, y=3 is the equation of a horizontal line that passes through the point (9, 3).

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Answer:

Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Step-by-step explanation:

To determine at which point Plan A is a better deal than Plan B, we need to compare the total cost of each plan for a given amount of data usage.

The total cost of Plan A for 3GB of data is $52 per month. For every additional GB of data, the cost is $3, so if we use x GB of data beyond the included 3GB, the total cost of Plan A would be $52 + $3x.

The total cost of Plan B for 5GB of data is $65 per month. For every additional GB of data, the cost is $1.75, so if we use x GB of data beyond the included 5GB, the total cost of Plan B would be $65 + $1.75x.

To determine at which point the total cost of Plan A is less than the total cost of Plan B, we can set the two equations equal to each other and solve for x:

$52 + $3x = $65 + $1.75x

$1.25x = $13

x = $13 / $1.25

x = 10.4

Therefore, Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

The solution to the equation are x=a

The given equation is sin (2x) = a and 0 < x < pi/2

Sin(2x) = sin x, 0≤x≤2п  ........................... (eq. 1)

Using the trigonometrical formula,

sin(2x) = sin xcosx

Let us subtract the formula from equation 1

2sinxcosx = sinx

Therefore, 2sinxcosx-sinx = 0

Let us remove common terms to get

sinx(2cox-1)=0

Now, sinx=0

x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]

Also, 2cos x =1

This means that cos x = 1/2

By implication, x=cos⁻¹(1/2)

That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

In conclusion, the value of [tex]\pi[/tex] is a as a single integer

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Answer: 12 miles

Step-by-step explanation:

Let y represent the cost and x represent the number of miles!

y = 1.25x + 3

Now put the $18 in for y

18= 1.25x + 3

15 = 1.25x

x = 12 miles

Answer:

Step-by-step explanation:

We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:

18 = 1.25x + 3

15 = 1.25x (subtracted 3 from both sides)

12 = x (divided each side by 1.25)

So, the trip was 12 miles

For the given conditions convention B attendance is decreasing at a greater rate.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the number of people attending convention A can be modeled by the function as,

f(x) = 1200 • 0.95ˣ

where x is the number of years that the convention has been occurring.

The number of people attending convention A in year 1,

f(x) = 1200 × 0.95¹

f(x) = 1140

The number of people attending convention A in year 2,

f(x) = 1200 × 0.95²

f(x) = 1083

The number of people decreasing in the Convention A,

=1140 - 1083

=57

If the number of people attending Convention B was 2200 in year 1 and 2100 in year 2. The number of people decreasing in the Convention B,

=2200-2100

=100

Thus, for the given conditions convention B attendance is decreasing at a greater rate.

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The given pair of equations has no solution.

Two equations can be solved through three different methods:

Let's use the elimination method in this question

                         20x - 4y = 11      .....(I)

                          10x - 2y = 6      .....(II)

Multiply (II) by 2

                          20x - 4y = 11      .....(I)

                          20x - 4y = 6      .....(II)

Now, subtracting equations (I) and (II) we will get no solution.

It is possible for the two lines to be parallel and not intersect. In this situation, we cannot identify a shared point between the two, and as a result, the system of the two equations representing the two lines cannot provide a solution!

This question is incomplete. The correct question is

Consider the two equations and solve for x and y.

                          20x - 4y = 11    

                          10x - 2y = 6  

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Answer:

first option

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 , then the 2 roots are real and irrational

• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational

• If b² - 4ac = 0 , then 2 roots are real and equal

• If b² - 4ac < 0 , then 2 roots are not real

3x² + 4x - 2 = 0 ← is in standard form

with a = 3, b = 4 and c = - 2 , then

b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40

since b² - 4ac > 0 , then 2 real and irrational roots

Answer:

2. d = 40; 2 rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:

[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)

             = 16 - (-24)

             = 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.