Two familie go to a zoo. The mith family of two adult and three children pay £61. The Jone family of three adult and five children pay £96. Work out the cot of an adult ticket and the cot of a child ticket

The function that represents the number of weeks with the height of the tomato plants is 4t - 25y = -150.

When the week has started, the height of the plant in inches is 6 inches.

So, one point can be (0,6).

Now, it is said that the plants grows at a rate of 16% per inches for several months.

So, it means that the slope of the equation is 0.16.

Now, we can use the point slope form of the line.

So, the required equation of the line is,

(y-6)/(t-0) = 0.16

y-6 = 0.16t

16t - 100y = -600

4t - 25y = -150

So, the above equation of line is the function that will relate number of weeks with the height of the plant.

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According to the evidence, we cannot conclude that the lower proportions of drowsiness in group 1 subjects is the side effect of the subjects in group 2., at alpha equals 0.05 level of significance. Thus, the correct option is C.

It is given that in the double-blind clinical trial, children are divided into two groups.

[tex]H_0 : p1=p2\\[/tex]

[tex]H_a: p1 > p2[/tex]

Now, N1= 450 , P1=136/450=0.3022

N2=95, P2=39/95=0.410

We have to now state the null and alternative hypotheses and draw conclusions based on them.

Now, the test statistics are done as follows:

Z= [tex]p1-p2/\sqrt{p1*1-p1/n1+p2*1-p2/n2}[/tex]

Z= [tex]0.3022-0.410/\sqrt{0.3022*1-0.3022/450+0.410*1-0.410/95}[/tex]

Z= [tex]-0.10/\sqrt{4.686+0.0025}[/tex]

Z= -0.10/2.165

Z= -0.04

At the significance level of 0.05.

Decision: We will reject the null hypothesis if the value of Z is less than the critical value

Critical value at Z(0.05)= -1.645

Thus, we will not reject the null hypothesis as the value of z is greater than the critical value. Thus, in this situation, we cannot conclude that the lower proportions of drowsiness in group 1 subjects as the side effect of the subjects in group 2.

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Some of the situations where we can apply parallel lines cut by transversal are mentioned below.

Transversal line is a line which cuts two or more coplanar lines. Coplanar lines are the lines which does not intersect each other.

The real life situations were we can apply parallel lines cut by transversal are:

Thus, in real life there are many situations where parallel lines cut by transversal.

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The doubles plus one fact for 7 7  is 7+7+1=15.

In layman's terms, Double Plus One Fact is a strategy for adding two consecutive numbers (numbers that are next to each other). To get the final result, simply add a smaller number to itself or double it and add 1.

Doubles fact are the numbers which are added with itself. such as 5+5=10, 3+3=6

so the doubles plus one fact are nothing but adding 1 to the result of doubles fact.

for given, doubles plus one fact for 7 7 is 7+7=14 and then adding 1 gives 14+1=15.

Hence, 7+7+1=15 is the doubles plus one fact for 7 7.

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The maximum degree of f(x) g(x) will be 14 and the minimum degreee of f(x) g(x) will be 0.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Function f(x) is a polynomial of degree 7,

And, g(x) is a polynomial of degree 7.

Now,

Since, Function f(x) is a polynomial of degree 7,

And, g(x) is a polynomial of degree 7.

Hence, The maximum degree of f(x) g(x) = 7 + 7 = 14

And, The minimum degree of f(x) g(x) = 0

Thus, The maximum degree of f(x) g(x) will be 14 and the minimum degree of f(x) g(x) will be 0.

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Research or Basic research is purely thoretical in  nature as its not easy to find its application in the real world. For example consider new theorems or  Formula in mathematics, its difficult to find their practical use right away as it takes time to find the fields where they may be applicable.

Practical research is more focused on solving a known problem hence its use is already known or easy to find as it is derived from real world only.

Like Research in development of new medicine is practical in nature as we know for whic disease we are trying to cure from it.

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Answer:

Step-by-step explanation:

Two different fractions where lowest common denominator is 20 are 1/4 and 1/5.

What are the lowest common denominator?

For two or more fractions, if the numbers at the bottom (or denominator) by which the lowest number can be divide into, is called the lowest common denominator. It is also known as the least common denominator.

Here, 20 is the given lowest common denominator. 

Therefore, we can write: 20 = 1 × 20, 20 = 2 × 10, 20 = 4×5

Hence, two fractions for which 20 can be a lowest common denominator are 1/4 and 1/5.

Hope it helps!

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).

Given that,

We have to find what kind of error is committed if the researcher doesn't rule out the null hypothesis even though it's incorrect.

We know that,

To determine whether the provided experimental results are valid, the null hypothesis is a type of hypothesis that explains the population parameter. Depending on the viability of the given population or sample, this hypothesis is either rejected or not.

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).

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Answer:

If a polygon is not a triangle, then the polygon has more than three sides. Since a triangle has exactly 3 sides, contrapositive is true

The Child and Dependent Care Credit is a tax credit that helps parents and families pay for the care of their children and other dependents while they work, are looking for work, or are going to school.

Childcare and nursing care costs money! Luckily, there are tax deductions to cover the costs. If you had to pay someone to care for your children, family members, or spouse, find a job, go to school, or because of a disability, Child and Dependent Care credits are available.

You are generally eligible for the Child and Caregiver Tax Credit if you meet all of the following conditions:

For year 2022, the Child and Caregiver Tax Credit is non-refundable. For eligible employment-related expenses, taxpayers can claim up to $3,000 for each eligible individual or one child, and up to $6,000 for two or more eligible individuals or children.

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The HL postulate states that two triangles are congruent if the hypotenuse and leg of one right triangle are congruent with the hypotenuse and leg of another right triangle.

Hypotenuse Leg Theorem

hypotenuse theorem proof shows how a given set of right triangles is congruent when the corresponding hypotenuses and one leg are of equal length.

Statement:

Two triangles are congruent by the hypotenuse leg theorem if the hypotenuse and one leg of a right triangle are congruent with the hypotenuse and leg of another right triangle.

given: where ABC is an isosceles triangle, AB = AC, and AD is perpendicular to BC.

Proof : AD as altitude is perpendicular to BC and forms ADB and ADC as right triangles. AB and AC are the respective hypotenuses of these triangles and we know they are equal. Because AD = AD is common for both triangles.

That is, AB = AC and AD is common.

Therefore, the hypotenuse and pair of legs of the two right-angled triangles satisfy the definition of the HL theorem.

We know that angles B and C are equal (property of isosceles triangle).

We also know that the angles BAD and CAD are equal (AD bisects BC and BD equals CD).

Therefore, △ADB ≅ △ADC

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A hypothesis is a statement regarding a characteristic of one or more populations. The null hypothesis is a statement of no change, no effect, or no difference. The alternative hypothesis is a statement we are trying to find evidence to support.

Generally, the null hypothesis expresses that there is no change, no difference, no effect, and in another way, no relationship between the independent and dependent variables. Because we are hypothesizing that nothing is happening, then it is called the null hypothesis.

The null and alternative hypothesis are two conflicting claims which researchers weigh evidence for and against using a statistical test. Null hypothesis (H0) means there is no effect in the population. Meanwhile, alternative hypothesis (Ha or H1) means there is an effect in the population.

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In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format. the leftmost bit is still reserved as the sign bit. a negative integer is just the complement of the positive integer, with a 1 in the leftmost spot to represent the negative sign

The method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm for addition and subtraction throughout the whole range

Changing the sign of any number is encoded by generating its complement, which is usually done by a very simple and efficient algorithm

Therefore, In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format.

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True , In any random sample drawn from a population, the sample mean is an unbiased estimator of the population mean.

What is the central limit theorem formula?

The central limit theorem gives a formula for the sample mean and the sample standard deviation when the population mean and standard deviation are known. This is given as follows: Sample mean = Population mean = μ μ Sample standard deviation = (Population standard deviation) / √n = σ / √n.

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Answer:

Below

Step-by-step explanation:

x values are the DOMAIN....for this equation 'x' can have any value :

 (- inf, + inf)

the y values that the function can have define the RANGE of the function. Due to the absolute value bars.....'y' can only be positive values or zero:

  [ 0 , + inf)

SAS: denotes the existence of two triangles whose two sides and included angle are known to be equal.

ASA: denotes the existence of two triangles whose included side and two known angles are equal.

SAS (side, angle, side):

Angle, Side, Angle, or ASA:

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The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.

Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.

There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.

As per the question,

With a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.

Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.

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In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function).

The number zero is not a real number. It is a mathematical notion used to symbolize an extremely huge value that is theoretically impossible to obtain. Limit solutions imply that the equation you are getting the limit of will continue to go in that direction indefinitely. The graph approaches but never touches the y-axis (represented by x = 0) because you have a vertical asymptote there. g(x) = 1/(x2) will continue to rise as you approach x = 0 from the right or left. You can picture it continuing upwards after it leaves the page. In other words, because g(x) keeps increasing indefinitely as x approaches 0, its limit is infinity.

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The required Cost of the bench will be $475

Let the cost of a garden table be $x

And the cost of a bench be  $y

Now, according to the question

Combined cost of garden table and bench are $1023

Therefore, we can write

x + y = 1023……….(i)

Now, again the cost of garden table is $73 more than that the cost of the bench

Therefore, we can write

x - y = 73………..(ii)

Subtracting equation (i) and (ii) we get

2x = 1096

x = 1096/2 = 548

x = 548

Putting the value of x in equation in (i) we get

y = 1023 - 548 = 475

Cost of garden table is $x = $548

Cost of bench is $y = $475

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In this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.

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, there are three different pencils that Monique possesses. She's interested in finding out what kind of pencil maintains its sharpness the longest. Each pencil she uses leaves an identical mark on a piece of paper.

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, in this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.

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Length of the actual tent is 15 feet.

Actual length is any distance between points that is not foreshortened by the view type.

Given that the scale of drawing is

1 inch : 5 feet

and length is 3 inches.

We have to find actual length of the tent.

Let us denote actual length of the tent by 'x'

We have by given data

3 inches : x = 1 inch : 5 feet

multiplying LHS by 3 we get,

3 : x = 3 : 15

By comparing both the sides

x = 15

Therefore the actual length of the tent is 15 feet.

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The example of descriptive statistics is d) 50% of the students surveyed spend at least two hours online each day.

Given:

a survey on internet usage was conducted among a group of 200 students in the school cafeteria. it was found that 100 students spend at least two hours online every day.

Here number of possible outcomes = 200

Number of favorable outcomes = 100

Probability p = 100/200

= 1/2

= 0.5

= 0.5*100%

= 50%

Therefore  50% of the students surveyed spend at least two hours online each day.

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Full question:

A survey on Internet usage was conducted among a group of 200 students in the school cafeteria. It was found that 100 students spend at least two hours online every day.Which of these is an example of descriptive statistics?a.) 50% of the students surveyed spend at least two hours online each day.b.) 50% of the students in the school spend at least two hours online each day.c.) 50% of the students in a class spend at least two hours online each day.d.) 50% of the students in the cafeteria spend at least two hours online each day.

The order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx

We need to switch the order of integration

I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy

From n = 0 to n = 4

y = 0 to y = n

Taken horizontal strip

on strip values of y will be fixed and values of x will be varied.

Limits of y are

y = 0 to y = 4

limits of x are

x = y to x = 4

I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy

I = ₀∫² ₀∫y² eˣ/y² dxdy

Taking vertical strip

on strip values of x will be fixed and values of x will be varied.

limits of x are

x = 0 to x = 4

Limits of y are

y = √x to y = 2

I = ₀∫⁴ √x∫y² eˣ/y² dydx

Therefore,  the order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx

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the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)

What is spherical coordinates?

The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.

Given (r,Ф,∅ ) = (3,0,0)

x = rsin∅ cosФ = 3 * sin0 *cos0 = 0

y =  rsin∅ sinФ = 3*0*0 = 0

z = rcos∅ = 3*1 = 3'

SO (x,y,y) = (0,0,3)

Hence the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)

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The final balance is $446.44

What is compound interest ?

Compound interest is when you add the interest you've already earned back into your principal balance, which increases your returns by compounding them. Consider that you have $1,000 in a savings account with a 5% annual interest rate. You would make $50 in the first year, giving you a new balance of $1,050.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 300.00(1 + 0.05/4)^(4)(8)

A = 300.00(1 + 0.0125)^(32)

A = 446.44

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Answer:

Its the Origin

Step-by-step explanation:

Its ZERO

Step-by-step explanation:

it depends on what the numbers are now if it's negative 10 and you're positive number is like over 10 then your number will be positive now if the negative number is more than the positive number then you know your answer is going to be negative so negative 10 - -5 is -5 so there would be your answer now if it was negative 10 - 20 that would be positive 10 does that make any sense

The cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Let the cost of 15 cups is x

3 → 7

15 → x

3/15 = 7/x

1/5 = 7/x

x = £35

The cost of 7 glasses:

= (24x7)/4

= £42

Thus, the cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.

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The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%

The fact that

The ratio of the event space's size to the sample space's size represents an event's probability.

The total number of outcomes equals the size of the sample space.

The number of outcomes in the event you are interested in is the event space.

so

P = event space size divided by sample space size

step 1

determine the likelihood that the person is over 40 years old.

The sample size is 255.

event space size = 85

P=85/255------> P=1/3

step 2

determine the likelihood that they consume root beer.

The sample size is 255.

event space size = 75

P=75/255------> P=5/17

step 3

determine the likelihood that the individual is over 40 years old or that

They consume root beer.

so

P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%

therefore, the response is

32/51 or 62.75%

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The final step in solving the given inequality is defining the range according to the final value of x as (-Inf,3).

In Variable based math, inequality is a numerical explanation that shows the connection between two articulations utilizing the imbalance image. The articulations on the two sides of a disparity sign are not equivalent. It implies that the articulation on the left-hand side ought to be more prominent than or not exactly the articulation on the right-hand side or the other way around.

On the off chance that the connection between two mathematical articulations is characterized utilizing the imbalance images, then it is called exacting disparities.

We have inequality as –2(5 – 4x) < 6x – 4

Step1: -10+8x<6x-4

Step2:8x-6x<-4+10

Step3:2x<6

Step4:x<3

Step5:Range of value of x as (-Inf,3)

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(Complete question) is:

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?