On a 800km trip, Ryan's family travelled at 90km/h for the first 600km and 100km/h for
the remainder of the journey. If they had travelled 90km/h for the entire journey, how
much longer would the trip have taken?

The value of the equation is y = 10 ( 8 + x ) = 80 + 10x , where y is the total cost of admission

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

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

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.

Given data ,

Let the equation be represented as A

Now , the value of A is

The cost of admission per student is c = $ 10

Let the total cost of admission be represented as y

Now , the number of students = 8 students

The number of additional students = x

So , the total cost of admission y = 10 ( x + 8 )

On simplifying the equation , we get

The total cost of admission y = 10x + 80

Now , if 6 more students go , the equation will be

The total cost of admission y₁ = 10 ( x + 6 + 8 )

On simplifying the equation , we get

The total cost of admission y₁ = 10x + 140

Hence , the equation is y = 10x + 80

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The required equation in slope intercept form is equal to y = -2x - 21.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

2x - y = -21

Making y the subject of formula in the above equation, we have the following:

y = -2x - 21

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There can be a maximum of 5 teams.Three persons will be excluded.

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to denote the logical syntax's operation order and other properties.

Considering that 23 pals gather to play a sport together.The participants must first be divided into teams. There must be exactly 4 participants on each team, and no one may play for more than one team.

The number of teams will be determined using the formulas below:

Total teams = 23 / 4 = 20 / 4 = 5.

Three persons will be left.

Therefore, there can be a maximum of 5 teams.Three persons will be excluded.

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To find the number of teams that can be made with 23 friends, where each team has exactly 4 players, we can divide the total number of friends by the number of players per team.

Number of friends = 23

Number of players per team = 4

To find the number of teams, we divide the number of friends by the number of players per team:

23 / 4 = 5 remainder 3

Since we cannot have a team with 3 players, we can only form complete teams of 4 players. Therefore, the maximum number of teams that can be formed is 5.

Therefore, the answer is 5 teams.

a)30*20 b)30*30 d)25*32 e)25*30 are NOT good ways to use compatible numbers to estimate the number of cans in the crates.

And the best expressions that is the good ways to use compatible numbers to estimate the number of cans in the crates is 32*27

As given in the question,

There are 32 crates. Each crate holds 27 cans of soup.

i.e. Number of total crates = 32

Number of can of soups in each crate = 27

The total number of cans of soup in every crates = 32*27

The total number of cans of soup in every crates = 864

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The answer to column 4 is a circle pattern that is shifted one unit up. This pattern consists of a series of overlapping circles that expand outward in a vertical direction.

To replace the question mark in column 4, you need to identify the pattern that is shifted one unit up. To do this, start by looking at the pattern in column 3 and imagining it shifted upwards one unit. This will give you the pattern for column 4. The pattern is a series of overlapping circles which expand outward in a vertical direction. To create the pattern, start by drawing a circle in the center of the column. Then, draw circles around the center circle that are slightly larger than the previous one. Repeat this process until the circles reach the edge of the column. This will create the circle pattern that is shifted one unit up. Finally, connect the circles with straight lines to create the full pattern. This pattern will replace the question mark in column 4.

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The complete question: which pattern should replace the question mark in column 4? this question is required. * circle pattern up one circle pattern down one

The probability that the student owns a credit card given that they are a freshman is 0.350  (3 d.p.)

[tex]Probability\: of\: an\: event\: occurring = \frac{Number\: of \:ways\:it\:can\:occur}{Total\:no.\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student owns a credit card

Use the given table to calculate the probability that the student is a freshman:

[tex]= > P(A)=\frac{60}{100} =0.6[/tex]

And the probability that the student is a freshman and owns a credit card:

[tex]= > P(A \cap B)=\frac{21}{100}=0.21[/tex]

To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of B given A is:

[tex]P(B |A)=\frac{P(A\cap B)}{P(A)}[/tex]

Substitute the found values into the formula:

[tex]P(B|A)=\frac{0.21}{0.6} =0.35[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35.

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The complete question is:

A group of students was asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.

Answer: 4.5 Days

Step-by-step explanation:

The work requires 9 men x 6 days or 54 man-days.

So 12 men will do the same work in 54 man-days/12 men

= 4.5 days.

I hope this is right sorry if its not

Answer:

The x intercept is -3

Step-by-step explanation:

To find the x intercept, let y = 0 and solve for x.

-5x-2y=15

-5x-2*0=15

-5x=15

Divide each side by -5

-5x/-5 = 15/-5

x = -3

The x intercept is -3

The unit rate of change in this situation is 0.25 mile per hour.

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The value of x and y of the first parallelogram is x = 7 and y = 9

The value of x and y of the second parallelogram is x = 3 and y = 6

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

a)

Let the first parallelogram be ABCD

Now , the opposite sides are parallel and opposite sides are congruent

So , The measure of AB = measure of CD

And , the measure of AD = measure of BC

Substituting the values in the equation , we get

3x - 5 = 2x + 2   be equation (1)

On simplifying the equation , we get

Subtracting 2x on both sides of the equation , we get

x - 5 = 2

Adding 5 on both sides of the equation , we get

x = 7

Now , 2y - 6 = y + 3   be equation (2)

On simplifying the equation , we get

Subtracting y on both sides of the equation , we get

y - 6 = 3

Adding 6 on both sides of the equation , we get

y = 9

Therefore , the value of x and y of the parallelogram is 7 and 9 respectively

b)

Let the second parallelogram be ABCD

Now , the the diagonals of a parallelogram bisect each other

Let O be the point of intersection of diagonals

So , The measure of AO = measure of CO

And , the measure of DO = measure of BO

Substituting the values in the equation , we get

2x + 5 = 11   be equation (1)

On simplifying the equation , we get

Subtracting 5 on both sides of the equation , we get

2x = 6

Divide by 2 on both sides of the equation , we get

x = 3

Now , y + 4 = 2x + 4   be equation (2)

On simplifying the equation , we get

Substitute the value of x = 3 in the equation , we get

y + 4 = 2 ( 3 ) + 4

y + 4 = 10

Subtracting 4 on both sides of the equation , we get

y = 6

Therefore , the value of x and y of the parallelogram is 3 and 6 respectively

Hence , the measures of parallelogram is solved

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It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.

This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.

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Answer:

D

Step-by-step explanation:

Option A has a dot on -25 and the arrows point from there to the left of the number line, going down from there. Representing x<-25.

Option B has a dot on -25 and the arrow goes to the right from there meaning it goes up. Representing x>-25

Option C has a dot on 25 and an arrow pointing to the left going down. Representing x<25

Finally, option D has a dot on 25 and an arrow pointing to the right meaning the number is going upward as intended by the question.

To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

What is a polynomial?

A polynomial is a mathematical expression that is a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and real or complex coefficients. The degree of a polynomial is the highest power of the variable. For example, the polynomial 3x^2 + 2x - 1 is a polynomial of degree 2, and the polynomial 5 is a polynomial of degree 0.

To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

For example, to find the zeroes of the polynomial 3x^2 + 2x - 1, we set the polynomial equal to zero:

3x^2 + 2x - 1 = 0

Then we can factor the polynomial or use the quadratic formula to find the solutions:

x = (-2 +/- sqrt(2^2 - 43(-1)) ) / (2*3) = (-2 +/- sqrt(4 + 12))/6 = (-2 +/- sqrt(16))/6 = (-1 +/- sqrt(4))/3 = (-1 +/- 2i)/3

The zeroes of the polynomial 3x^2 + 2x - 1 are x = (-1 + 2i)/3 and x = (-1 - 2i)/3, which are complex numbers.

Hence, To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

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Decimal: 369.3125  Binary: 101111001.0101  Octal: 571.5  Hexadecimal: 171.A8. The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows:  Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8.

Decimal: 10111101.101  Binary: 10111101.101  Octal: 277.125  Hexadecimal: BD.1A

Decimal: 326.5  Binary: 10100010.1  Octal: 502.1  Hexadecimal: 142.8

Decimal: F3C7.A82  Binary: 1111001111100111.10101000010  Octal: 36367.5212  Hexadecimal: F3C7.A82

To convert a number from one base to another, we can use the following steps:

1. Identify the number and its base.

2. Convert the number to its equivalent in decimal form.

3. Convert the decimal form of the number to the desired base.

For example, to convert the number 369.3125 from decimal to binary, octal, and hexadecimal, we can follow these steps:

1. Identify the number and its base: 369.3125 is a decimal number.

2. Convert the number to its equivalent in decimal form: 369.3125 is already in decimal form, so we don't need to convert it.

3. Convert the decimal form of the number to the desired base:

Binary: 101111001.0101

Octal: 571.5

Hexadecimal: 171.A8

The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows:  Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8. Similarly, the number 10111101.101 can be converted to binary, octal, and hexadecimal as follows: Binary: 10111101.101, Octal: 277.125, Hexadecimal: BD.1A. Finally, the number 326.5 can be converted to binary, octal, and hexadecimal as follows: Binary: 10100010.1, Octal: 502.1, Hexadecimal: 142.8, and the number F3C7.A82 can be converted to binary, octal, and hexadecimal as follows: Binary: 1111001111100111.10101000010, Octal: 36367.5212, Hexadecimal: F3C7.A82.

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the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

an = 3*2^(n-1) + 1

The sequence appears to follow a pattern of 3*2^n + 1

Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1. (Note that n begins with 1, so we subtract 1 from n.)

The nth term an of the sequence 3, 10, 29, 66, 127, can be expressed as 3*2^(n-1) + 1. This follows a pattern of multiplying the previous term by 2 and then adding 1. For example, the second term 10 is 3*2^1 + 1, and the third term is 3*2^2 + 1. This pattern continues for each term in the sequence, which begins at n=1. Therefore, the expression for the apparent nth term an of the sequence is 3*2^(n-1) + 1.

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A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.

The P=0.04 defines that if the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner.

Drawing random samples from the population on each occasion, then, on 4% of occasions, you would get the same or greater difference between groups.

In statistical hypothesis testing, we need to express the null hypothesis, which is the no statistical difference within the groups, and the alternative hypothesis, which is the statistical difference.

Then, we determine the test statistic, which is a standardized quantitative measure of the group difference.

The null hypothesis predicts that the test statistic value will be small, but there is a slight possibility that it will be big by chance. We utilize the test statistic to compute the p-value once we determine the test statistic.

The p-value is described as the calculated probability of determining the observed result from the value of the test statistic, or larger, under the null hypothesis.

Therefore, we can conclude that the value of the definition of the p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.

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The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed.

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The interval notation, which describes a set of numbers by using values enclosed in brackets, can be used to express the domain and range. When writing intervals, we place a square bracket around the endpoint when it is part of the set and a parenthesis around it if it is not or if the interval is unbound.

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The expression for the total number of pages Millie and Lee read each day is 225 + 155.

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

Mille = 225 pages

Lee = 155 pages

The expression to find the total number of pages Millie and Lee read each day is given by the sum of the individual pages

i.e. p = 225 + 155

So, the expression to find p is p = 225 + 155.

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We will examine the 30-60-90 triangle concept in this session and learn everything there is to know about it, including its formula, definition, sides, area, and the rules that apply to this triangle.

A 30-60-90 triangle is a special sort of right triangle that always has angles that are 30, 60, and 90 degrees.

The angles of the triangles ABC and PQK in this instance are 30°, 60°, and 90°, respectively.

The side opposing the 30° angle, AB = y, will always be smaller because 30° is the triangle's smallest angle.

The side opposing the 60° angle, BC = y 3 = y 3, will be of medium length because 60° is the triangle's mid-sized degree angle.

The hypotenuse AC = 2y will be the greatest side on the side across from the 90° angle because 90° is the largest angle.

Considering that the Pythagorean Theorem is given by:

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Complete question -

The correct option is e. (Necessarily False) It required by the court to seek counselling

Because it is given as a fact that the child was "required by the court to seek counselling" ; and there is already P -> Q statement; where P : A child is released with no charges. and Q : Child is NOT required by the court to seek counseling. Taking the negation of this [tex]$\sim Q \Longrightarrow \sim P$[/tex]

[tex]$\sim P:$[/tex]Child is released with some charge.

If your child is arrested for a criminal offence and they are under 18, the police must tell you as soon as possible. The police should not interview your child until you are present, unless a delay would mean an immediate risk of harm to someone or serious loss of, or damage to, property.

Legal Counselling is the process by which a lawyer communicates advice to a client. I cannot emphasize anymore over the fact that it is the duty of an advocate to fearlessly uphold the interests of his client by all fair and honorable means without regard to any unpleasant consequences to himself or any other.

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Answer:

Step-by-step explanation:

we first have to remove the 3 years as it is the difference

then when we divide it we get the age of yeboah=10

as akua is 3 years older we add the3 to the 10= 13

the product is = 10×13=130

The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.

448

Q(m) is the least positive integer such that for every n ≥ Q(m), there is a perfect cube k^3 in the range n < k^3 ≤ m.

For example, Q(2) = 1 since 1^3 is in the range 1 < 1^3 ≤ 2.

Similarly, Q(3) = 2 since 2^3 is in the range 2 < 2^3 ≤ 3, and Q(4) = 3 since 3^3 is in the range 3 < 3^3 ≤ 4.

We are asked to find the remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000.

To do this, we can calculate the sum of the first 2017 terms of the sequence.

Q(2) + Q(3) + Q(4) + ... + Q(2017) = 448

Since 448 is divisible by 1000, the remainder when the sum is divided by 1000 is 0.

The remainder when the sum Σ 2017 m=2 Q(m) is divided by 1000 is 448.

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The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.

In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property. To determine this property, we can look at the two-dimensional transformation above, where y = ax + b. In order for the PDFs of x and y to be the same, the linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1.In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.

The complete question is : g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y = ax + b, are to be the same?

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Answer:

$5.25

Step-by-step explanation:

Original cost of cheese = $4.20

An increase in price of 25% means the cost increase = 25% of $4.20

25% in decimal = 25/100 = 0.25 (or 1/4)

25% of $4.20 = 0.25 x $4.20 = $1.05

or, if you are more comfortable working with fractions
25% of $4.20 =  1/4 x $4.20 = $1.05

This is only the cost increase.

Add this increase to the original cost to get the new price:

New price = $4.20 + $1.05 =$5.25

They have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.

50t = 40(t+1)

10t = 40

They are not travelling in the same way. They would cross paths in 4 hours if they were travelling in the same direction.

Before the NY train departs for Boston, a Boston train goes 40 miles.

After they have both travelled a total of 160 miles, they will now combine.

40x+50x=160

90x=160

x=16/9

1:46:40

After they have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.

They will get together at 5:46:40.

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Answer:

1) 84

2) 83160

Step-by-step explanation:

Greatest common divisor and Least common multiple

840 = 2³ * 3 * 5 * 7

8316 = 2² * 3³ * 7 * 11

i) The greatest whole number that will divide both 840 and 8316 is the

Greatest common divisor. Find only the common factors.

Greatest common divisor = 2² * 3 * 7

                                          = 84

84 is the greatest whole number that divides both 840 and 8316.

Answer: 84

ii) The smallest non-zero whole number that is divisible by 840 and 8316 is Least common multiple of 840 & 8316.

Least common multiple = 2³ * 3³ * 5 * 7 * 11

                                        = 8 * 27 * 5 * 7 * 11

                                        =83160

An integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75 is  1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt.

We have been given two functions representing the displacement of the particle,

x(t)=2cos(πt)

y(t)=4sin(πt)

To find the velocity vector with the help of these functions, we have to differentiate them with respect to time

i.e,

dx(t)/dt=d{2cos(πt)}/dt=-2sin(πt)

dy(t)/dt=d{4sin(πt)}/dt=4cos(πt)

and finally, the velocity vector would be written as,

v(t)=-2sin(πt) i +4cos(πt) j

Now to get the distance for the given limits we have to integrate the magnitude of the given velocity

i.e, integrate 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt

which would approximately result in a value of 3.69 units in length.

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Answer:

I honestly hv iyiu u ughu ugvjug uyvbuyg uugbjug niyhnig mhyij. umnninji. oh jiuh